Wave dynamics on time-depending graph with Aharonov-Bohm ring
https://doi.org/10.17586/2220-8054-2018-9-4-457-463
Abstract
Aharonov–Bohm ring (AB ring) is an element frequently used in nanosystems. The paper deals with wave dynamics on quantum graph consisting of AB ring coupled to a segment. It is assumed that the lengths of the edges vary in time. Variable replacement is made to come to the problem for stationary geometric graph. The obtained equation is solved using the expansion with respect to a complete system of eigenfunctions of the unperturbed self-adjoint operator for the stationary graph. The coefficients of the expansion are found as solutions of a system of differential equations numerically. The influence of the magnetic field is studied. The comparison with the case of stable geometric graph is made.
Supporting agencies: This work was partially financially supported by the Government of the Russian Federation (grant 08-08), by grant 16-11-10330 of Russian Science Foundation.
About the Authors
D. A. Eremin
Ogarev Mordovia State University
Russian Federation
Russian Federation
Department of Mathematics and IT
Bolshevistskaya Str. 68, Saransk
E. N. Grishanov
Ogarev Mordovia State University
Russian Federation
Russian Federation
Department of Mathematics and IT
Bolshevistskaya Str. 68, Saransk
D. S. Nikiforov
ITMO University
Russian Federation
Russian Federation
Department of Higher Mathematics
Kroverkskiy pr. 49, St. Petersburg, 197101
I. Y. Popov
ITMO University
Russian Federation
Russian Federation
Department of Higher Mathematics
Kroverkskiy pr. 49, St. Petersburg, 197101
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Review
For citations:
Eremin D.A., Grishanov E.N., Nikiforov D.S., Popov I.Y. Wave dynamics on time-depending graph with Aharonov-Bohm ring. Nanosystems: Physics, Chemistry, Mathematics. 2018;9(4):457-463. https://doi.org/10.17586/2220-8054-2018-9-4-457-463
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